Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties

Saša Novaković

Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties

Algebraic Geometry 2018-04-06 v2

Authors: Saša Novaković

Abstract

We classify absolutely split vector bundles on proper $k$ -schemes. More precise, we prove that the closed points of the Picard scheme are in one-to-one correspondence with indecomposable absolutely split vector bundles. Furthermore, we apply the obtained results to study the geometry of (generalized) Brauer--Severi varieties.

Keywords

absolutely split vector bundles proper k-schemes Picard scheme Brauer-Severi varieties locally free sheaves indecomposable bundles

Cite

@article{arxiv.1501.00859,
  title  = {Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties},
  author = {Saša Novaković},
  journal= {arXiv preprint arXiv:1501.00859},
  year   = {2018}
}

Comments

17 pages, revised version with corrected and improved result, comments are welcome!

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